{
  "id": "1908.08372",
  "version": "v1",
  "published": "2019-08-22T13:41:20.000Z",
  "updated": "2019-08-22T13:41:20.000Z",
  "title": "Hyperbolicity of coarse moduli spaces and isotriviality for certain families",
  "authors": [
    "Ya Deng"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "In this paper, we prove the Kobayashi hyperbolicity of the coarse moduli spaces of canonically polarized or polarized Calabi-Yau manifolds in the sense of complex $V$-spaces (a generalization of complex $V$-manifolds in the sense of Satake). As an application, we prove the following hyperbolic version of Campana's isotriviality conjecture: for the smooth family of canonically polarized or polarized Calabi-Yau manifolds, when the Kobayashi pseudo-distance of the base vanishes identically, the family must be isotrivial, that is, any two fibers are isomorphic. We also prove that for the smooth projective family of polarized Calabi-Yau manifolds, its variation of the family is less than or equal to the essential dimension of the base.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-22T13:41:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q45",
      "32G13",
      "14D22",
      "14D07",
      "14J15"
    ],
    "keywords": [
      "coarse moduli spaces",
      "polarized calabi-yau manifolds",
      "hyperbolicity",
      "campanas isotriviality conjecture",
      "hyperbolic version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}